SudoCue - Minimum Windoku Collection

The program I wrote to find Sudoku-X puzzles with the minimum number of 12 (probably) clues has been adapted to broaden the search to other variants, such as Windoku with a current 11 clues minimum and Windoku-X with a current 9 clues minimum.
This page will keep you informed about the progress of the Windoku search and you can download collections with essentially unique Windoku puzzles in their minimal form, so far all of them with only 11 clues.

This Windoku starts with a series of 26 empty cells. It has only 11 clues and a unique solution.
It can be solved with relatively simple techniques, as long as you keep the extra constraints in mind.

Puzzles

You can download a zip with the current collection of 18778 windoku puzzles with 11 clues.

Search method

I started with 40000 Windoku puzzles from my puzzle generator with 15 or fewer clues. With this collection, I performed the following steps:

• Remove each of the existing clues in turn, and place digits 1 through 9 one by one in each empty cell, skipping the cell just cleared.
• Check the validity of each of the resulting puzzles and all valid puzzles to the collection
• Canonicalize the collection and remove any duplicates
• Remove the clues for each puzzle one by one and when any of them have a unique solution, remove the original and add the new puzzle(s) with 1 clue less
• When sufficient puzzles with N-1 clues have been collected, remove all puzzles with N or more clues
• Repeat these steps until no new puzzles can be added

Using this method, the first 11 clue results quickly appeared. Unlike Windoku-X, this variant is slowing down rapidly in the discovery of new 11 clues puzzles from the 12 clues collection, so I decided to give it new input. Hopefully there will be more results soon.

Canonicalization method

The dihedral group (reflection & rotation) gives 8 equivalent puzzles. These transformations do not change the relative position of cells, but only operate on the complete puzzle.
Swapping rows 2 and 3, rows 7 and 8, columns 2 and 3, columns 7 and 8 gives 16 (2 ^ 4) permuations, without altering the groups to which each cell belongs.
Swapping rows 1 and 4, rows 6 and 9, columns 1 and 4, columns 6 and 9 swaps the 9 boxes with the 9 windoku groups (also keeping the diagonals intact). This doubles the number of permutations.

For each of the 256 (8 * 16 * 2) available transformations, the clues are renumbered in order of appearence and compared with the best result so far, replacing it when better.

I will continue to look for more 11-clue puzzles, as long as some progress can be made. If you like to contribute any 11-clue Windoku puzzles that you have found, I will gladly add them to the collection.